Further dimensions: text, typography and play in the metaverse

In this text I wish to delve into the creation of textual content as well as its visualization through typographic design mechanisms inside three dimensional virtual worlds, which are known as the metaverse. I am particularly focused upon the way in which such virtually three dimensional environments may place the usage of text within a context that stands in contradiction to its traditional one by creating an unexpected novel purpose which takes a marked departure from the intrinsic attribute with which text has inherently been associated – namely the attribute of readability. In such environments readability, or indeed even legibility, may often be displaced through the usage of text and typography as a playful device, as artifacts which may manifest in puzzle-like configurations, or as visual structures the contents of which are meant to be understood through means other than straightforward reading; thus bringing about states of heightened engagement, wonder and ‘play’ through their manipulation or indeed simply by being immersed within the spaces which are brought about through their very agency. I also wish to expand upon this subject by talking about my own experiments with this material and will conclude by positing that further virtual dimensions can be instrumental in eliciting exciting alternative usages of text and typography which bring to the fore the allographic properties of text as an artistic/creative expressive media that may well bear further scrutiny and exploration

Discrete Gravitational Dimensions

We study the physics of a single discrete gravitational extra dimension using the effective field theory for massive gravitons. We first consider a minimal discretization with 4D gravitons on the sites and nearest neighbor hopping terms. At the linear level, 5D continuum physics is recovered correctly, but at the non-linear level the theory becomes highly non-local in the discrete dimension. There is a peculiar UV/IR connection, where the scale of strong interactions at high energies is related to the radius of the dimension. These new effects formally vanish in the limit of zero lattice spacing, but do not do so quickly enough to reproduce the continuum physics consistently in an effective field theory up to the 5D Planck scale. Nevertheless, this model does make sense as an effective theory up to energies parametrically higher than the compactification scale. In order to have a discrete theory that appears local in the continuum limit, the lattice action must have interactions between distant sites. We speculate on the relevance of these observations to the construction of finite discrete theories of gravity in four dimensions.Comment: 5 pages, 4 diagrams. Important typos in some equations corrected; conclusion s unchange

Constructing Gravitational Dimensions

It would be extremely useful to know whether a particular low energy effective theory might have come from a compactification of a higher dimensional space. Here, this problem is approached from the ground up by considering theories with multiple interacting massive gravitons. It is actually very difficult to construct discrete gravitational dimensions which have a local continuum limit. In fact, any model with only nearest neighbor interactions is doomed. If we could find a non-linear extension for the Fierz-Pauli Lagrangian for a graviton of mass mg which does not break down until the scale Lambda_2=(mg Mpl)^(1/2), this could be used to construct a large class of models whose continuum limit is local in the extra dimension. But this is shown to be impossible: a theory with a single graviton must break down by Lambda_3 = (mg^2 Mpl)^(1/3). Next, we look at how the discretization prescribed by the truncation of the KK tower of an honest extra diemsinon rasies the scale of strong coupling. It dictates an intricate set of interactions among various fields which conspire to soften the strongest scattering amplitudes and allow for a local continuum limit. A number of canditate symmetries associated with locality in the discretized dimension are also discussed.Comment: 21 pages, 6 diagrams, 1 figur

(De)Constructing Dimensions

We construct renormalizable, asymptotically free, four dimensional gauge theories that dynamically generate a fifth dimension.Comment: 10 pages, late

Disordered Extra Dimensions

A very large extra dimension may contain many localized branes. We discuss the possibility to formulate such models as a spin system where each spin indicates the supersymmetry direction preserved by the corresponding brane. In the evolution of the universe, the extra dimensions might have ended into a vacuum made of patches with different orientation of the spins, responsible for the observed breaking of supersymmetry. We discuss the limit where the separation of these patches is by very thin defects described as localization of gravitino masses.Comment: 15 pages, no figure. Typos corrected. References added. Version accepted for publication

Topological mass in seven dimensions and dualities in four dimensions

The massive topologically and self dual theories en seven dimensions are considered. The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in four dimensions.Comment: 7 page